How do you solve the equation $x^2+x+1/4=9/16$ by completing the square?

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Answer 1 · 2017-01-27T09:14:43

$x=1/4" or "-5/4$

rearrange as follows

$x^2+x=9/16-1/4$

$x^2+x=5/16$

complete the square $LHS$

$(x^2+x+(1/2)^2)-(1/2)^2=5/16$

$(x+1/2)^2-1/4=5/16$

now solve for $x$

$(x+1/2)^2=5/16+1/4=9/16$

$(x+1/2)^2=9/16$

$x+1/2=+-sqrt(9/16)$

$x+1/2=+-3/4$

$x=-1/2+-3/4$

$x_1=-1/2+3/4=1/4$

$x_2=-1/2-3/4=-5/4$

How do you solve the equation x^2+x+1/4=9/16x^2+x+1/4=9/16 by completing the square?